The EU visa of your son has nothing to do with Turkey and the Turkish border officials wouldn't even care about it. Turkey is not in the Schengen zone or the EU so this is nothing to bother with.
Also for your 14 year old son, does he have an existing Turkish e-visa or are we speaking about another visa. By the way, mfa.gov.tr is the official government site of the Ministry of Foreign Affairs and I would trust that rather than any external source.